Here's my submission:
=A1&MOD(10-MOD(SUMPRODUCT(MID(A1,ROW($1:$12),1)*(1+2*ABS(MOD( ROW($1:$12),2)-1))),10),10)

My hat is off to whoever provided the original formula: I learned a lot
today. Very clever!

Strongly recommended to test against samples that are known to be
correct.